{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 实验题目 4：牛顿迭代法"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 问题分析\n",
    "\n",
    "> 准确描述并总结出实验题目（摘要），并准确分析原题的目的和意义。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 方法概要"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "已知非线性方程 $f(x) = 0$，求其根 $x^*$。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 实验目的\n",
    "\n",
    "利用牛顿迭代法求 $f(x) = 0$ 的根。\n",
    "\n",
    "**输入：** 初值 $\\alpha$，精度 $\\varepsilon_1,\\varepsilon_2$，最大迭代次数 $N$\n",
    "\n",
    "**输出：** 方程 $f(x) = 0$ 根 $x^*$ 的近似值或计算失败标志"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 数学原理\n",
    "\n",
    "> 数学原理表达清晰且书写准确。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 牛顿迭代法"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "求非线性方程 $f(x)=0$ 的根 $x^*$，牛顿分析法计算公式："
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "x_0 = \\alpha , \\ x_{n+1} = x_n - \\frac{f(x_n)}{f'(x_n)}, \\ n = 0,1,\\cdots\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "一般地，牛顿迭代法具有局部收敛性，为了保证迭代收敛，要求，对充分小的 $\\delta, \\alpha \\in O(x^*,\\delta)$。如果 $f(x) \\in C^2[a,b],f(x^*) = 0, f'(x^*) \\ne 0$，那么，对充分小的 $\\delta > 0$，当 $\\alpha \\in O(x^*, \\delta)$ 时，由牛顿迭代法计算出的 $\\{x_n\\}$ 收敛于 $x^*$，且收敛速度是 2 阶的；如果 $f(x) \\in C^m[a,b],f(x^*) = f'(x^*)=\\cdots =f^{(m-1)}(x^*)=0$，$f^{(m)}(x^*)\\ne 0 (m > 1)$，那么，对充分小的 $\\delta > 0$，当$\\alpha \\in O(x^*,\\delta)$时，由牛顿迭代法计算出的$\\{x_n\\}$收敛于$x^*$，且收敛速度是 1 阶的。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 牛顿迭代法的几何意义\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![几何意义](imgs/newton01.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "由上图所示，方程 $f(x)=0$ 的根 $\\alpha$ 是曲线 $y=f(x)$ 与直线 $y=0$ 的交点的横坐标。牛顿迭代法是取过 $(x_i,f(x_i))$ 点的切线方程\n",
    "\n",
    "$$\n",
    "y = f(x_i) = f'(x_i)(x-x_i)\n",
    "$$\n",
    "\n",
    "与 $y = 0$ 的交点的横坐标\n",
    "\n",
    "$$\n",
    "x_{i+1} = x_i - \\frac{f(x_i)}{f'(x_i)}\n",
    "$$\n",
    "\n",
    "作为根的新的近似值。由此往复，只要初值取得接近根 $\\alpha$，$\\{x_0,x_1,\\cdots,x_n\\}$ 会很快收敛于 $\\alpha$。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 程序设计流程\n",
    "\n",
    "> 编译通过，根据输入能得到正确输出。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 引入需要的包\n",
    "import numpy as np\n",
    "from pandas import DataFrame\n",
    "from matplotlib import pyplot as plt\n",
    "from typing import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "def newton(\n",
    "        f: Callable[[float], float],\n",
    "        f_: Callable[[float], float],\n",
    "        alpha: float,\n",
    "        N: int,\n",
    "        epsilon_1: float,\n",
    "        epsilon_2: float,\n",
    "        *args,\n",
    "        **kwargs):# -> Optional[float]:\n",
    "    history: List[float] = []\n",
    "    n = 1\n",
    "    x = alpha\n",
    "    while n <= N:\n",
    "        history.append(x)\n",
    "        v, v_ = f(x), f_(x)\n",
    "        if abs(v) < epsilon_1:\n",
    "            return x, history\n",
    "        if abs(v_) < epsilon_2:\n",
    "            return None, history\n",
    "        x_ = x - v / v_\n",
    "        if abs(x_ - x) < epsilon_1:\n",
    "            history.append(x_)\n",
    "            return x_, history\n",
    "        n = n + 1\n",
    "        x = x_\n",
    "    return None, history"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_history(title: str, history: List[float]):\n",
    "    plt.figure(dpi=150)\n",
    "    plt.title(title)\n",
    "    plt.plot(range(len(history)), history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_question(*args, **kwargs):\n",
    "    res, history = newton(*args, **kwargs)\n",
    "    if res is None:\n",
    "        print(\"拟合失败!\")\n",
    "    else:\n",
    "        print(f\"x^* = {res:.4f}\")\n",
    "    show_history(kwargs.get('title', ''), history)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "问题 1 (1)\n",
      "x^* = 0.7391\n",
      "问题 1 (2)\n",
      "拟合失败!\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# 问题一\n",
    "def question_1():\n",
    "    print(\"问题 1 (1)\")\n",
    "    run_question(\n",
    "        f=lambda x: np.cos(x) - x,\n",
    "        f_=lambda x: -np.sin(x) - 1,\n",
    "        alpha=np.pi / 4,\n",
    "        N=10,\n",
    "        epsilon_1=1e-6,\n",
    "        epsilon_2=1e-4,\n",
    "        title=\"$Q_1 (1): \\\\cos{x} - x = 0, \\\\alpha = \" + f\"{np.pi / 4:.9f}\" + \"$\")\n",
    "    print(\"问题 1 (2)\")\n",
    "    run_question(\n",
    "        f=lambda x: np.exp(-x) - np.sin(x),\n",
    "        f_=lambda x: -np.exp(x) - np.cos(x),\n",
    "        alpha=0.6,\n",
    "        N=10,\n",
    "        epsilon_1=1e-6,\n",
    "        epsilon_2=1e-4,\n",
    "        title=\"$Q_1 (2): e^{-1}-\\\\sin{x} = 0, \\\\alpha = 0.6$\")\n",
    "\n",
    "\n",
    "question_1()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "问题 2 (1)\n",
      "x^* = 0.5671\n",
      "问题 2 (2)\n",
      "x^* = 0.5666\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# 问题二\n",
    "def question_2():\n",
    "    print(\"问题 2 (1)\")\n",
    "    run_question(\n",
    "        f=lambda x: x - np.exp(-x),\n",
    "        f_=lambda x: 1 + np.exp(-x),\n",
    "        alpha=0.5,\n",
    "        N=10,\n",
    "        epsilon_1=1e-6,\n",
    "        epsilon_2=1e-4,\n",
    "        title=\"$Q_2 (1): x-e^{-x}=0, \\\\alpha = 0.5$\")\n",
    "    print(\"问题 2 (2)\")\n",
    "    run_question(\n",
    "        f=lambda x: x**2 - 2 * x * np.exp(-x) + np.exp(-2 * x),\n",
    "        f_=lambda x: -2*np.exp(-2*x) - 2*np.exp(-x) + 2*x + 2*np.exp(-x)*x,\n",
    "        alpha=0.5,\n",
    "        N=10,\n",
    "        epsilon_1=1e-6,\n",
    "        epsilon_2=1e-4,\n",
    "        title=\"$Q_2 (2): x^2-2xe^{-x}+e^{-2x} = 0, \\\\alpha = 0.5$\")\n",
    "\n",
    "\n",
    "question_2()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 实验结果\n",
    "\n",
    "> 准确规范地给出各个实验题目的结果，并对相应的思考题给出正确合理的回答与说明。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "由问题 1 输出、图像可知：\n",
    "\n",
    "1. 第一问在第二次迭代即收敛到目标精度，得结果 $x^* = 0.7391$（保留四位小数）\n",
    "2. 第二问在 $N$ 次数内收敛失败"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "由问题 2 输出、图像可知：\n",
    "\n",
    "1. 第一问在第二次迭代即收敛到目标精度，得结果 $x^* = 0.5671$（保留四位小数）\n",
    "2. 第一问在第七次迭代才收敛到目标精度，得结果 $x^* = 0.5666$（保留四位小数）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**思考题：**\n",
    "\n",
    "1. *对实验 1，确定初值的原则是什么？实际计算中应如何解决？*\n",
    "\n",
    "    初值如果选择得偏离根太远，很可能出现迭代次数过多或者发散的情况。因此，初值最好选择在靠近根的位置。在实际计算中，如果仅仅使用牛顿迭代法收敛定理来选择初始值，往往比较复杂，一般使用简化方法：\n",
    "\n",
    "    对方程 $f(x) = 0$，如果\n",
    "    $$\n",
    "    f''(x_0)\\ne 0, |f'(x_0)|^2>|\\frac{f(x_0)f''(x_0)}{2}|\n",
    "    $$\n",
    "    则可以保证大多数情况下的牛顿迭代法的收敛性。\n",
    "2. *对实验 2，如何解释在计算中出现的现象？试加以说明*\n",
    "\n",
    "    由于牛顿迭代法的收敛阶都是 $2$，而第二问所求函数是第一问的平方，即 $f_2(x) = f_1^2(x)$，平方后的函数的斜率相对原来小许多，所以第二问中收敛就比第一问慢。\n",
    "\n"
   ]
  }
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